[Back] The Z3 library was developed by Microsoft Research and can be used as a prover/solver. In this case we use Z3 to solve a suduko puzzle:

Matrix: (0,0,0,2,6,0,7,0,1),(6,8,0,0,7,0,0,9,0),(1,9,0,0,0,4,5,0,0),(8,2,0,1,0,0,0,4,0),(0,0,4,6,0,2,9,0,0),(0,5,0,0,0,3,0,2,8),(0,0,9,3,0,0,0,7,4),(0,4,0,0,5,0,0,3,6),(7,0,3,0,1,8,0,0,0)

A zero value identifies a space. Examples:

In this case we start with:

and the answer is:

The following example is taken from the Z3 Web site [here]:

from z3 import * # 9x9 matrix of integer variables X = [ [ Int("x_%s_%s" % (i+1, j+1)) for j in range(9) ] for i in range(9) ] # each cell contains a value in {1, ..., 9} cells_c = [ And(1 <= X[i][j], X[i][j] <= 9) for i in range(9) for j in range(9) ] # each row contains a digit at most once rows_c = [ Distinct(X[i]) for i in range(9) ] # each column contains a digit at most once cols_c = [ Distinct([ X[i][j] for i in range(9) ]) for j in range(9) ] # each 3x3 square contains a digit at most once sq_c = [ Distinct([ X[3*i0 + i][3*j0 + j] for i in range(3) for j in range(3) ]) for i0 in range(3) for j0 in range(3) ] sudoku_c = cells_c + rows_c + cols_c + sq_c # sudoku instance, we use '0' for empty cells instance = ((0,0,0,2,6,0,7,0,1), (6,8,0,0,7,0,0,9,0), (1,9,0,0,0,4,5,0,0), (8,2,0,1,0,0,0,4,0), (0,0,4,6,0,2,9,0,0), (0,5,0,0,0,3,0,2,8), (0,0,9,3,0,0,0,7,4), (0,4,0,0,5,0,0,3,6), (7,0,3,0,1,8,0,0,0)) if (len(sys.argv)>1): instance=eval("("+sys.argv[1]+")") print "The solution is:" instance_c = [ If(instance[i][j] == 0, True, X[i][j] == instance[i][j]) for i in range(9) for j in range(9) ] s = Solver() s.add(sudoku_c + instance_c) if s.check() == sat: m = s.model() r = [ [ m.evaluate(X[i][j]) for j in range(9) ] for i in range(9) ] print_matrix(r) else: print "failed to solve"